The TSA will not cut the locks off unless something looks like a bomb on their scanners. There are also special locks available now that can be opened by the TSA if necessary. You can also run a cable tie through one of the zippers and put your lock through the cable tie and the other zipper to secure your luggage.

cable ties come in very handy bring a handful literally. I used the colored ones to secure all my suitcase locks. If security needs to get into bag for some reason, they will cut tie and then replace with a tranluscent white one. Having started with colors, you will know if a bag has been opened.
1.) Colored cable ties, a big handful
2.) Nail clipper--in carry on--
I can't tell you how many times I have "locked" my luggage with a tie, then decided I needed something in the bag, or forgot to put an item in--so bring lots!

the cable ties work great! We use them to secure our bags for flying. Bring extra- tuck them into an outside zippered compartment on your checked-bag, tuck some more and nailclippers in your carry-on luggage.